Cn中单位球上的Qp空间,n-1/n＜p≤1

Cn中单位球上的Qp和Qp,0空间分别定义为

Qp Spaces in the Unit Ball of Cn with n-1/n＜p≤1

The holomorphic function spaces Qp and Qp.0 on the unit ball B of Cn are defined as Qp = {fholomorphic;sup a∈B∫B | f|2(z)Gp(z,a)dλ(z) ＜∞ } and Qp,0= {f holomorphic;lim|z|→1∫B | f|2(z)Gp(z,a)dλ(z) ＜ 0}.In this paper, we characterize holomorphic functions f(z) to be of Qp(or Qp,0) for n - 1/n ＜ p ≤ 1 in terms of p-Carleson (or vanishing p-Carleson) measures with f(z), f(z), Rf(z) and ∑1≤i＜j≤n | Ti,jf(z)| respectively. As an application of our theory we can answer an open question proposed by Ouyang.